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Journal of Convex Analysis 27 (2020), No. 1, 227--236
Copyright Heldermann Verlag 2020

Existence and Uniqueness of Solutions for an Integral Perturbation of Moreau's Sweeping Process

Giovanni Colombo
Dip. di Matematica, Università di Padova, 35121 Padova, Italy

Christelle Kozaily
INRIA Rennes -- Bretagne Atlantique, 35042 Rennes, France

We prove existence and uniqueness of solutions for a sweeping process driven by a prox-regular moving set with an integral forcing term, where the integrand is Lipschitz with respect to the state variable. The problem is motivated by a model introduced by Brenier, Gangbo, Savaré and Westdickenberg [Sticky particle dynamics with interactions, J. Math. Pures Appl. 99 (2013) 577--617]. The proof is based on a general type of penalization.

Keywords: Evolution equations, moving sets, prox-regular sets, differential inequalities

MSC: 34G25.

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